Chaos Synchronization and Chaos Anticontrol of a Rotationally Supported Simple Pendulum

Abstract

Chaos synchronization and anticontrol of a rotationally supported simple pendulum was studied in this paper. Different kinds of coupling terms are used to synchronize the two identical chaotic systems with different initial conditions. An observed-based scheme is also used to achieve synchronization. The results are demonstrated by phase portrait, Lyapunov exponent, Poincaré maps and synchronization time. Next, in order to analyze the transient behavior of the synchronized systems, Euclidean distance is used to plot a figure with coupling strength versus the distance. The chaotic signals are used to mask the message function in the secure communication system. Finally, anticontrol of chaos is achieved by adding constant term, periodic term, impulse term, time-delay term and adaptive control.